$string = '"LastName, FirstName" ([samaccountname])'
[Regex]::Matches($string, '(?<=\")(.*?)(?=\")').Value
Uses a regex expression with find all characters that match the expression.
PS C:\> $string = '"LastName, FirstName" ([samaccountname])' >> [Regex]::Matches($string, '(?<=\")(.*?)(?=\")').Value LastName, FirstName